In designing electromagnetic filters having multiple resonant elements, it is desirable to control the strength and nature of coupling between adjacent resonant elements in the interest of determining particular coupling bandwidths for the filter. The strength of the coupling is represented by the magnitude of the coupling coefficient k, which is defined as follows: EQU k=k.sub.H -k.sub.E,
wherein k.sub.H and k.sub.E represent the magnetic and electric coupling coefficients, respectively. The extent to which the respective magnetic and electric fields generated by each resonant element interact determines the magnitudes of k.sub.H and k.sub.E, respectively. If k is positive, the coupling has a magnetic nature, while if k is negative, the coupling has an electric nature.
Typical bandpass filters, for example, include multiple resonant elements separated by interior walls of a filter housing where each interior wall has an aperture to permit a certain amount of coupling between adjacent resonant elements. The aperture in the interior wall separating the adjacent resonant elements allows a limited amount of interaction between the electromagnetic fields generated by the adjacent resonant elements. If no interior wall separates the resonant elements, the strength and nature of the coupling is determined merely by coupling cancellation, thereby providing limited design flexibility.
As shown in FIGS. 1A and 1B, a portion of a prior bandpass filter designed to achieve magnetic coupling includes a filter housing 10 having a cover 12, a first side wall 14, a second side wall 16, a bottom wall 18, a back wall 20, and a front wall 22 (FIG. 1B). The portion of the bandpass filter further includes two resonant cavities 24, 26 defined by an interior wall 28. The two resonant cavities 24, 26 each include a split-ring resonator 30 mounted on a face of the cover 12 by a mounting mechanism 32. Assuming that some signal source (not shown) provides a signal to one of the two resonant cavities 24, 26, coupling between the two resonant cavities 24, 26 would occur through a slot aperture 34 (FIG. 1B) disposed in the interior wall 28 as shown. The slot aperture 34 does not, however, provide a sufficient amount of magnetic coupling for some filter specifications.